目录

一、二叉搜索树简介

二、二叉搜索树的结构与实现

2.1二叉树的查找与插入

2.2二叉树的删除

2.3二叉搜索树的实现

2.3.1非递归实现

 2.3.2递归实现

三、二叉搜索树的k模型和kv模型

一、二叉搜索树简介

二、二叉搜索树的结构与实现

2.1二叉树的查找与插入

2.2二叉树的删除

2.3二叉搜索树的实现

2.3.1非递归实现

//二叉树节点的构建
template<class K>struct BSTreeNode{typedef BSTreeNode<K> Node;Node* _left;Node* _right;K _key;BSTreeNode(const K& key):_left(nullptr), _right(nullptr), _key(key){}};//class BinarySearchTreetemplate<class K>class BSTree{typedef BSTreeNode<K> Node;public:// 强制生成默认构造BSTree() = default;//拷贝构造BSTree(const BSTree<K>& t){_root = Copy(t._root);}//赋值拷贝BSTree<K>& operator=(BSTree<K> t){swap(_root, t._root);return *this;}//析构函数~BSTree(){Destroy(_root);}/////增删查改//插入数据bool Insert(const K& key){if (_root == nullptr){_root = new Node(key);return true;}Node* parent = nullptr;Node* cur = _root;while (cur){if (cur->_key < key){parent = cur;cur = cur->_right;}else if (cur->_key > key){parent = cur;cur = cur->_left;}else{return false;}}cur = new Node(key);if (parent->_key < key){parent->_right = cur;}else{parent->_left = cur;}return true;}//查找数据bool Find(const K& key){Node* cur = _root;while (cur){if (cur->_key < key){cur = cur->_right;}else if (cur->_key > key){cur = cur->_left;}else{return true;}}return false;}//删除数据bool Erase(const K& key){Node* parent = nullptr;Node* cur = _root;while (cur){if (cur->_key < key){parent = cur;cur = cur->_right;}else if (cur->_key > key){parent = cur;cur = cur->_left;}else{if (cur->_left == nullptr){if (cur == _root){_root = cur->_right;}else{if (cur == parent->_right){parent->_right = cur->_right;}else{parent->_left = cur->_right;}}delete cur;return true;}else if (cur->_right == nullptr){if (cur == _root){_root = cur->_left;}else{if (cur == parent->_right){parent->_right = cur->_left;}else{parent->_left = cur->_left;}}delete cur;return true;}else{// 替换法Node* rightMinParent = cur;Node* rightMin = cur->_right;while (rightMin->_left){rightMinParent = rightMin;rightMin = rightMin->_left;}cur->_key = rightMin->_key;if (rightMin == rightMinParent->_left)rightMinParent->_left = rightMin->_right;elserightMinParent->_right = rightMin->_right;delete rightMin;return true;}}}return false;}private：Node* _root;};

 2.3.2递归实现

//二叉树节点的构建
template<class K>struct BSTreeNode{typedef BSTreeNode<K> Node;Node* _left;Node* _right;K _key;BSTreeNode(const K& key):_left(nullptr), _right(nullptr), _key(key){}};//class BinarySearchTreetemplate<class K>class BSTree{typedef BSTreeNode<K> Node;public:// 强制生成默认构造BSTree() = default;//拷贝构造BSTree(const BSTree<K>& t){_root = Copy(t._root);}//赋值拷贝BSTree<K>& operator=(BSTree<K> t){swap(_root, t._root);return *this;}//析构函数~BSTree(){Destroy(_root);}/////增删查改bool FindR(const K& key){return _FindR(_root, key);}bool InsertR(const K& key){return _InsertR(_root, key);}bool EraseR(const K& key){return _EraseR(_root, key);}void InOrder(){_InOrder(_root);cout << endl;}private：void Destroy(Node* root){if (root == nullptr)return;Destroy(root->_left);Destroy(root->_right);delete root;}Node* Copy(Node* root){if (root == nullptr)return nullptr;Node* newRoot = new Node(root->_key);newRoot->_left = Copy(root->_left);newRoot->_right = Copy(root->_right);return newRoot;}//借助引用可以更好的删除和更改数据节点，不需要再额外创建父节点来更改bool _EraseR(Node*& root, const K& key){if (root == nullptr)return false;if (root->_key < key){return _EraseR(root->_right, key);}else if (root->_key > key){return _EraseR(root->_left, key);}else{Node* del = root;if (root->_right == nullptr){root = root->_left;}else if (root->_left == nullptr){root = root->_right;}else{Node* rightMin = root->_right;while (rightMin->_left){rightMin = rightMin->_left;}swap(root->_key, rightMin->_key);return _EraseR(root->_right, key);}delete del;return true;}}bool _InsertR(Node*& root, const K& key){if (root == nullptr){root = new Node(key);return true;}if (root->_key < key){return _InsertR(root->_right, key);}else if (root->_key > key){return _InsertR(root->_left, key);}else{return false;}}bool _FindR(Node* root, const K& key){if (root == nullptr)return false;if (root->_key < key){return _FindR(root->_right, key);}else if (root->_key > key){return _FindR(root->_left, key);}else{return true;}}void _InOrder(Node* root){if (root == nullptr)return;_InOrder(root->_left);cout << root->_key << " ";_InOrder(root->_right);}Node* _root;};

三、二叉搜索树的k模型和kv模型

// 改造二叉搜索树为KV结构
template<class K, class V>
struct BSTNode{BSTNode(const K& key = K(), const V& value = V()): _pLeft(nullptr) , _pRight(nullptr), _key(key), _Value(value){}BSTNode<T>* _pLeft;BSTNode<T>* _pRight;K _key;V _value};
template<class K, class V>
class BSTree{typedef BSTNode<K, V> Node;typedef Node* PNode;
public:BSTree(): _pRoot(nullptr){}PNode Find(const K& key);bool Insert(const K& key, const V& value)bool Erase(const K& key)
private:PNode _pRoot;};void TestBSTree()
{// 输入单词，查找单词对应的中文翻译BSTree<string, string> dict;dict.Insert("string", "字符串");dict.Insert("tree", "树");dict.Insert("left", "左边、剩余");dict.Insert("right", "右边");dict.Insert("sort", "排序");// 插入词库中所有单词string str;while (cin>>str){BSTreeNode<string, string>* ret = dict.Find(str);if (ret == nullptr){cout << "单词拼写错误，词库中没有这个单词:" <<str <<endl;}else{cout << str << "中文翻译:" << ret->_value << endl;}}
}